Second‐kind Fredholm integral‐equation analysis of scattering by layered dielectric gratings

Abstract

Scattering of the E-polarised plane electromagnetic wave from two different but of the same-period all-dielectric rectangular bar gratings on substrates is analysed using a volume-integral-equation (VIE) method. Here, VIE is a Fredholm integral equation of the second kind with unknown function being the electric field in the gratings regions. Discretisation of the VIE is performed by applying an entire-domain Galerkin technique. The developed algorithm possesses guaranteed convergence, provides accuracy, and is easily controlled by the order of discretisation. Numerical results for frequency-selective reflection, manipulation of light to propagate in prescribed directions, and the ultrahigh-Q lattice-modes resonances are presented and discussed.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Computation of TM Scattered Fields Induced by a Truncated Semi-Elliptic Cavity in a PEC

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“…As can be seen in Figure 2, the electric field $${\vert E}_{z}\vert $$ for both cases converges as M increases. To show the convergence behaviour of the unknown coefficients, we also plotted the truncation error of the series coefficient $${C}_{m}$$ in Figure 2c for the large cavity case [17]. As illustrated in Figure 2c, when $$M$$ increases, first the truncation error increases then decreases rapidly.…”

A simple yet efficient solution for TE scattering from a right trapezoidal groove

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